I How to rule out that the speed of light was different in the past?

[Vanadium 50]

@victorvmotti , for your question to make sense in a scientific sense, there must be some way to measure it. Please tell us how to measure what the sped of light was 2000 years ago, or 2 million, or 2 billion. Take your pick.

 

[Nugatory]

@victorvmotti , for your question to make sense in a scientific sense, there must be some way to measure it. Please tell us how to measure what the sped of light was 2000 years ago, or 2 million, or 2 billion. Take your pick.

To be fair, his question is basically "How can we be so sure it hasn't changed if we can't measure it?"

 

[Vanadium 50]

α is absolutely not the speed of light morphed into a dimensionless form.
Insofar as it is anything at all besides α, it is the charge of the electron morphed into a dimensionless form.

c is a factor that comes about because we historically measured time in seconds and length in meters. (And is equal to a dimensionless 1 in sane units). It's a conversion factor, like the dozen. No more, no less. It tells us about spacetime, not electromagnetism.

 

[Dale]

Yes, but then do the permittivity and permeability ratio of vacuum (free space) could be different some billions of years ago?

This runs into the same problem that I mentioned previously, it is just not so obvious:

A change in c that leaves α unchanged produces no change in an experiment designed to measure the speed of light. In contrast, a change in α without a change in c does produce a change in such an experiment.

The same thing happens with $\epsilon_0$ or any other dimensionful universal constant for EM.

 

[victorvmotti]

@victorvmotti , for your question to make sense in a scientific sense, there must be some way to measure it. Please tell us how to measure what the sped of light was 2000 years ago, or 2 million, or 2 billion. Take your pick.

After reading the responses here and elsewhere, and noting the repeated emphasis on the fine structure constant by the Physics Forums community mentors, I'd say we can measure it in the past indirectly. So, assuming that other dimensionful constants involved in this particular ratio known as $\alpha$ were not different in the past, say in 2 billion years ago, we can refer to the data from the Oklo mine natural nuclear reactor. And it looks like we have experimental evidence here on our planet from at least 2 billion years ago, ruling out that the speed of light was different in the past!

 

[vanhees71]

α is absolutely not the speed of light morphed into a dimensionless form.
Insofar as it is anything at all besides α, it is the charge of the electron morphed into a dimensionless form.

c is a factor that comes about because we historically measured time in seconds and length in meters. (And is equal to a dimensionless 1 in sane units). It's a conversion factor, like the dozen. No more, no less. It tells us about spacetime, not electromagnetism.

No, the charge of the electron is defined to be $-e$ in the SI. As detailed in #27 the ingredient of $\alpha$ that's not defined since 2019 by defining the units s, m, kg, and A, is the "permittivity of the vacuum", $\epsilon_0$ which is now to be measured. The same holds for the "permeability of the vacuum", $\mu_0$, which now is no longer defined but has to be measured. In the SI before 2019 (since 1948 or so) $\mu_0$ was defined through the definition of the A via the force of two infinitelylong straight wires of negligible width: $\mu_0^{(\text{old})}=4 \pi \cdot 10^{-7} \text{N} \cdot \text{A}^{-2}$. Now it's to be measured and the current value is $μ_0^{(\text{new})} = 1.25663706212(19) \cdot 10^{-6} \text{N}\cdot \text{A}^{-2}$.

 

[Vanadium 50]

To be fair, his question is basically "How can we be so sure it hasn't changed if we can't measure it?"

Then I would argue that if you can't tell, you're free to use any units you want.

 

[Sagittarius A-Star]

Yes, but then do the permittivity and permeability ratio of vacuum (free space) could be different some billions of years ago?

I think there is a redundancy between the three "constants of nature" in
$c= \frac{1}{\sqrt{\epsilon_0 \mu_0}}$. Only two of them are needed. The third is only calculated from the other two and could be substituted in all physics books. I would regard $\mu_0$ as least important, because the magnetic field is only a Lorentz-transformed electric field and there exist no magnetic monopoles.

 

[vanhees71]

It's a matter of definition, and within the SI $c$ is defined, and both $\epsilon_0$ and $\mu_0$ must be measured somehow. It's of course enough to measure one of them and then use the relation to $c$ to calculate the other.

Historically it was the other way around: the analogue of $\epsilon_0$ and $\mu_0$ was known in the 19th century from measuring the relation of the charge in electrostatic and magnetostatic units (Kohlrausch and Weber 1855, measuring the charge on a Leiden bottle by measuring forces on test charges (electrostatic measurement) and comparing it to the magnetic flux due to the current when discharging it (magnetostatic measurement)).

Then famously Maxwell discovered his equations of the electromagnetic field, i.e., he added the "displacement current" to the Ampere Law, as it was known from action-at-a-distance models (e.g., a la Neumann) at the time, and predicted the existence of electromagnetic waves with a phase velocity given by the said relation between electrostatic and magnetostatic units of charge, which is analogous to $c=1/\sqrt{\epsilon_0 \mu_0}$ when using SI units. The resulting value was pretty close to the then known speed of light, so that Maxwell could conjecture that light might be just electromagnetic waves.

 

[BWV]

How do we know that a dozen was twelve in the past?

Its not translation-invariant, some locations around me it is 13 or 14, depending on whether bagels or donuts are involved

 

[hutchphd]

I think it makes it worse and not better. It mixes the fundamental with the practical.

Then I would argue that if you can't tell, you're free to use any units you want.

That was my point

 

[Vanadium 50]

permeability ratio of vacuum

Is an artifact of our system of units. (This was clearer under the older definitions) Did you think it was a measured quantity and just happened to be 4π? Gosh, what are the chances of that!

The c that comes here is the same c in the Lorentz force law (and is 1 for suitable choice of velocity units).

Maybe the way to think about it is this way. Back when solving trig identities, the teacher said that \sin^2 \phi + \cos^2 \phi is "just a fancy way of writing 1". In exactly the same way, 300,000 m/s is "just a fancy way of writing 1". Asking whether it was different in the past is the same as asking if the number 1 was different in the past.

Just as 1 meter to the left is the same as 1 meter up, 300,000 meters is the same as 1 second.

 

[member 728827]

Asking whether it was different in the past is the same as asking if the number 1 was different in the past.

I think that observations from distant Galaxies (which is kind of looking into the past), don't rule out that c was different (compared to our local and current environment).

 

[PeterDonis]

I think that observations from distant Galaxies (which is kind of looking into the past), don't rule out that c was different (compared to our local and current environment).

Why do you think that?

 

[member 728827]

Why do you think that?

Because is my understanding that the concept of the "uniformity" of c is a local concept, and could be not so "uniform" at the cosmological level. And for "local" I mean in the spacetime sense.

 

[PeroK]

Because is my understanding that the concept of the "uniformity" of c is a local concept, and could be not so "uniform" at the cosmological level. And for "local" I mean in the spacetime sense.

It makes no sense to say that the local $c$ here is different from the local $c$ there. This, again, is where you need a change that affects the observed physical phenomena - like the spectrum of hydrogen.

 

[Grinkle]

my understanding that the concept of the "uniformity" of c is a local concept

Perhaps you are conflating locally flat spacetime with what you call uniformity of c.

 

[member 728827]

It makes no sense to say that the local $c$ here is different from the local $c$ there. This, again, is where you need a change that affects the observed physical phenomena - like the spectrum of hydrogen.

As I said, "here" and "there" are spacetime concepts at the cosmological level in the context I'm talking. If I'm not wrong (that would be no surprise for me anyway), even Einstein considered that GR was "locally" correct, but...

And there's an open debate about the "redshift" of Quasars...

 

[member 728827]

Perhaps you are conflating locally flat spacetime with what you call uniformity of c.

Outside the "locality" environment - which I'm unable to say if it's 1 billion YL or whatever -, who knows? It's not obvious, and the scientific data about Quasars and Galaxies is an open debate.

 

[Dale]

So, assuming that other dimensionful constants involved in this particular ratio known as α were not different in the past, say in 2 billion years ago, we can refer to the data from the Oklo mine natural nuclear reactor. And it looks like we have experimental evidence here on our planet from at least 2 billion years ago, ruling out that the speed of light was different in the past!

Yes. However, if you are assuming that $c$ could vary then it is a little odd to assume that none of the other constants in $\alpha$ can vary. To me, that assumption is objectionable.

Since we are detecting a possible variation in $\alpha$ it is far better (in my opinion) to simply measure it and report any variation than to try to assert that such variation in $\alpha$ corresponds to a variation in $c$.

 

[victorvmotti]

Since we are detecting a possible variation in $\alpha$ it is far better (in my opinion) to simply measure it and report any variation than to try to assert that such variation in $\alpha$ corresponds to a variation in $c$.

So back again to your point earlier. It is impossible, logically, to know if the speed of light was different in the past or not!

 

[Dale]

So back again to your point earlier. It is impossible, logically, to know if the speed of light was different in the past or not!

Right. We can experimentally test for variations in $\alpha$, and all of the physics are captured by that. Anything further that we try to say specifically about $c$ is just an assumption.

Since $$\alpha=\frac{e^2}{2 \epsilon_0 h c}$$ we can take a non-variation in $\alpha$ to mean that $c$ has doubled and $h$ has halved!

 

[hutchphd]

To me, that assumption is objectionable.

Well of course big claims demand axtraordinary evidence. But the Hubble redshift assertions do make a tempting target!

 

[Vanadium 50]

little odd to assume that none of the other constants in can vary.

Especially because c is present in the definition of the fine structure constant in some systems of units and not others.

In MKSA, \alpha = e^2/2\epsilon_0 hc. If it varies, my money is on the 2 changing. After all, LEP at CERN measured the number 3 experimentally and got 2.99 +/- 0.01.

 

[Sagittarius A-Star]

Einstein considered that GR was "locally" correct, but...

Do you have a related link?

And there's an open debate about the "redshift" of Quasars...

If you refer to the "tired light" hypothesis, there exists evidence against it, for example

The tired light model does not predict the observed time dilation of high redshift supernova light curves. This time dilation is a consequence of the standard interpretation of the redshift: a supernova that takes 20 days to decay will appear to take 40 days to decay when observed at redshift z=1.

Source:
https://astro.ucla.edu/~wright/tiredlit.htm

 

[PeterDonis]

is my understanding that the concept of the "uniformity" of c is a local concept

Where are you getting that understanding from? Please give a reference.

 

[PeterDonis]

there's an open debate about the "redshift" of Quasars...

What open debate? Please give a reference.

 

[vanhees71]

Right. We can experimentally test for variations in $\alpha$, and all of the physics are captured by that. Anything further that we try to say specifically about $c$ is just an assumption.

Since $$\alpha=\frac{e^2}{2 \epsilon_0 h c}$$ we can take a non-variation in $\alpha$ to mean that $c$ has doubled and $h$ has halved!

No! Since 2019 we can't do this, because $c$, $h$, and $e$ are fixed within the SI to define the units used to do measurements. What's not defined but must be measured is now $\epsilon_0$! So using the new SI it's $\epsilon_0$ that may have changed with time. So far there's no hint at such a variation modulo the (high) accuracy in measuring spectral lines from far-distant objects.

 

[apostolosdt]

I wonder if the following article makes any sense under the current discussion about the speed of light history: https://cds.cern.ch/record/618057/files/0305457.pdf

 

[Dale]

No! Since 2019 we can't do this, because c, h, and e are fixed within the SI to define the units used to do measurements.

Sure we could. We could just use non-SI units.